You actually caught an error... yes... the speed to catch up is 8.5 mph and not 11.7 mph.

People in the ebike world tend to use Watthours because that's how we think of our batteries. Cyclists tend to use things like calories. I'm going to stay in the ebike world for my numbers if that's okay. Basically a watthour is just a watt applied for an hour, so it's easy when you are dealing with motor output that is normally in watts.

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Let's start to include things like the motor heating and the resulting inefficiencies that they might add to the problem. We do the calculations again (with the correction) and now we adjust the motor for higher heating and higher loads so that rather than 70% efficiency we use a figure like 60%. (which is pretty realistic for a motor asked to work 172.3 watt / 139.5 watt = 24% more power)



Downhill (5% negative slope for 10 miles)

Freewheel - 10 miles / 24.35 mph = 0.41 hours (net power gain/loss is zero)

Regen - 10 miles / 15.00 mph = 0.67 hours (behind by 0.26 hours)

Recaptured Energy = 0.133 hp * 746 watt = 99.22 watt

99.22 watt * 0.67 hours = 66.48 Wh * 0.7 (motor losses) = 46.5 Wh

46.5 Wh * 0.9 (battery losses) = 42 Wh (this is the energy recovered)



Uphill (5% positive slope for 10 miles)

Freewheel - 10 miles / 7 mph = 1.43 hours

Power Needed - 0.187 hp * 746 watt = 139.5 watt / 0.7 (motor losses) = 199.3 watt

199.3 watt * 1.43 hours = 285 Wh

Regen - Must do 10 miles in 1.43 hours - 0.26 hours = 1.17 hours

10 miles / 8.5 mph = 1.17 hours

Power Needed - 0.231 hp * 746 watt = 172.3 watt / 0.6 (motor losses) = 287.2 watt

246.2 watt * 1.17 hours = 336 Wh

...but we get to subtract the "savings" so the actual value is:

336 Wh - 42 Wh = 293 Wh


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So now they balance again.... slight advantage to the freewheel...


The truth is going to come down to the efficiency of the regen system. The better the efficiency the more likely that someone can break even or get ahead. The lower the efficiency the more certain that regen loses.


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Another factor is gears... are we to allow gears with regen? How does one implement it? We know that with a freewheel you can use multispeed gearing that's critical to getting your efficiency up higher.

So would we want to explore more "real" situations that involve actual hub motors using regen and compare them to multispeed freewheel bikes on the same track?

This is where I've gone with my simulation program (which I'm still tinkering with) in that it uses real motors and gives results about real things.


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In principle there is the potential for regen to make sense... but does it in practice?

How many one speeds have won the Tour De France lately? (hub motors are one speeds)

If you use a hub motor that is designed to go faster then it will tend to have lowered efficiency when climbing hills. Choose a slower top speed setup for your hub motor and hill climbing is better, downhill regen is good, but you are then restricted on the flat to slower speeds.

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